Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

The influence of wear paths produced by hip replacement patients during normal walking on wear rates

Variation in wear paths is known to greatly affect wear rates in vitro, with multidirectional paths producing much greater wear than unidirectional paths. This study investigated the relationship between multidirectional motion at the hip joint, as measured by aspect ratio, sliding distance, and wear rate for 164 hip replacements. Kinematic input from three-dimensional gait analysis was used to determine the wear paths. Activity cycles were determined for a subgroup of 100 patients using a pedometer study, and the relationship between annual sliding distance and wear rate was analyzed. Poor correlations were found between both aspect ratio and sliding distance and wear rate for the larger group and between annual sliding distance and wear rate for the subgroup. However, patients who experienced a wear rate <0.08 mm/year showed a strong positive correlation between the combination of sliding distance, activity levels, and aspect ratio and wear rate (adjusted r2?=?55.4%). This group may represent those patients who experience conditions that most closely match those that prevail in simulator and laboratory tests. Although the shape of wear paths, their sliding distance, and the number of articulation cycles at the hip joint affect wear rates in simulator studies, this relationship was not seen in this clinical study. Other factors such as lubrication, loading conditions and roughness of the femoral head may influence the wear rate.

Fronts, jumps and secondary introductions suggested as different invasion patterns in marine species, with an increase in spread rates over time

Not all introduced (invasive) species in a region will spread from a single point of introduction. Long-distance dispersal or further introductions can obscure the pattern of spread, but the regional importance of such processes is difficult to gauge. These difficulties are further compounded when information on the multiple scale process of invasive species range expansion is reduced to one-dimensional estimates of spread (e. g. km yr(-1)). We therefore compared the results of two different metrics of range expansion: maximum linear rate of spread and accumulation of occupied grid squares (50 x 50 km) over time. An analysis of records for 54 species of introduced marine macrophytes in the Mediterranean and northeast Atlantic revealed cases where the invasion process was probably missed (e. g. Atlantic Bonnemaisonia hamifera) and suggested cases of secondary introductions or erratic jump dispersal (Dasysiphonia sp. and Womersleyella setacea). A majority of species analysed showed evidence for an accumulation of invaded sites without a clear invasion front. Estimates of spread rate are increasing for more recent introductions. The increase is greater than can be accounted for by temporally varying search effort and implies a historical increase in vector efficiency and/or a decreased resistance of native communities to invasion.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

From the UV to the static-field limit: rates and scaling laws of intense-field ionization of helium

We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.

THE EFFECT OF VARYING COSMIC-RAY IONIZATION RATES ON DARK CLOUD CHEMISTRY

We investigate the effects of varying the cosmic ray ionization rate in chemical models of dense interstellar clouds. In the absence of such ionization, a scenario which may be applicable to dark cloud cores, we find that chemi-ionization is able to drive a limited ion-neutral chemistry. Models of clouds in starburst galaxies, which may have enhanced cosmic ray fluxes, are also investigated and enable an upper limit to be derived for the cosmic ray ionization rate in M82. The derived value, which is about 700 times the typical value for Galactic molecular clouds, is in good agreement with that necessary to explain the recent observations of C I in this galaxy.